Alzamastry

It's the pathstones that light the streets with soft crystal glows.
It's the intangible cats that prowl around every human's feet.
It's the wispy flickers of a ghostly form passing down the hall.
Alzamastry is an umbrella term for the study of all the inter-related metaphysical aspects of the world. This field of study began in the 11th century, with the invention of pathstones by Andalusi scholar Al-Zahrawi (Also known as Abulcasis in Europe). The field originally studied only pathstones and the language used to control them, but over the centuries, connections to other topics have been brought in. For example, the energy that powers pathstones comes from the movement of ghosts, so the study of ghosts became a subtopic of Alzamastry.
A natural philosopher who studies alzamastry is called an Alzamatrist. Most Alzamatrists have one or two subtopics that they specialize in.

Crystalogy

Demonym: Crystalogist

A crystalogist specializes in pathstones. They might focus on the crystals themselves, such as identifying types of crystals that could work as pathstones, finding and extracting the crystals in the earth (Field crystalogy), or focus on the creation and inscription of formulas in pursuit of new uses for pathstones (linguistic crystalogy). Almost all crystalogists have at least some experience with both sides of the field, but have chosen to specialize in their preferred area.
Field crystalogists can become quite wealthy by operating mines and supplying crystals to various governments and businesses. The bulk of linguistic crystalogists create pathstones from known formulas and are employed to maintain existing pathstones.
At the Palais d'Or, the headquarters of the prestigious La Société Royale de l'Alzamastrie, the more academic linguistic crystalogists work on deciphering Babelian and discovering new phrases to unlock new uses for pathstones. These theoretical linguistic crystalogists are responsible for some of the world's most impressive technological breakthroughs and are highly regarded.

Psychopompology

Demonym: Psychopompologist

Psychopompologists are most known for stubbornly insisting that they are called psychopompologists and not "cat experts". These alzamatrists study soul guides, which primarily come in the form of cats in Europe. They are nearly nonexistent in Catholic or Orthodox countries, where soul guides are seen as evil and driven away.
Studying soul guides incorporates the study of fate due to how a soul guide reflects the future of its human. This branch of alzamastry is therefore tightly wound with religion as practitioners attempt to incorporate their findings with what their religion teachers about fate or destiny. They say that when arguments echo down the hall of the Palais d'Or, nine times out of ten it's the psychopompologists going at it again.

Animalogy

Demonym: Animalogist

Animalogists have nothing to do with animals and everything to do with souls. They specialize in the study of ghosts and their movement into the afterlife. An animalogist might not know how to create a pathstone, but they would know exactly where the nearest death pathway is to charge it.
Outside the library, animalogists can be found lurking around allegedly haunted places to try to learn more, or traipsing across fields to map the smallest feeder routers for the bigger highways of the dead. They are concerned with what substance makes up a ghost's form, what rules outline a ghost's appearance, how is energy transferred from a ghost into a pathstone, and many more questions regarded human souls postmortem.
The most haunted locations in the world are the labs of animalogists due to the number who elect to remain in the world rather than move on in order to study ghosts from the other side. Still-living animalogists often come into their labs in the morning to find theories scrawled by a phantom hand on their slate boards, and often build up a friendly rapport with their ghostly lab partner.

Etymology

From the Arabic الزُّمُرُّدُ‎ (al-zamarad), "emerald". Alzamastry as a field began with the study and creation of pathstones, which were originally all emeralds.